Stability coriolis mass flow meter

ABSTRACT

An optimized Coriolis mass flow meter is disclosed which has improved stability to excitations caused by external influences. A primary source of improvement involves determining by modal analysis of the flow conduit a location for the sensor means that minimizes the influence of external excitation of one or more of the first in phase bending mode, the first out of phase bending mode, the first out of phase twist mode, the second out of phase twist mode, the second out of phase bending mode and the third out of phase bending mode.

BACKGROUND OF THE INVENTION

This application is a continuation-in-part of our U.S. patentapplication Ser. No. 364,032 filed Jun. 9, 1989 now abandoned.

In the art of measuring mass flow rates of flowing substances it isknown that flowing a fluid through an oscillating flow conduit inducesCoriolis forces which tend to twist the conduit in a directionessentially transverse to the direction of fluid flow and also to theaxis about which oscillation occurs. It is also known that the magnitudeof such Coriolis forces is related to both the mass flow rate of thefluid passing through the conduit and the angular velocity at which theconduit is oscillated.

One of the major technical problems historically associated with effortsto design and make Coriolis mass flow rate instruments was the necessityeither to measure accurately or control precisely the angular velocityof an oscillated flow conduit so that the mass flow rate of the fluidflowing through the flow conduits could be calculated using measurementsof effects caused by Coriolis forces. Even if the angular velocity of aflow conduit could be accurately determined or controlled, precisemeasurement of the magnitude of effects caused by Coriolis forces raisedanother severe technical problem. This problem arose in part because themagnitude of generated Coriolis forces is very small in comparison toother forces such as inertia and damping, therefore resulting Coriolisforce-induced effects are minute. Further, because of the smallmagnitude of the Coriolis forces, effects resulting from externalsources such as vibrations induced, for example, by neighboringmachinery or pressure surges in fluid lines, may cause erroneousdeterminations of mass flow rates. Such error sources as discontinuitiesin the flow tubes, unstable mounting of the tubes, use of tubes lackingmechanically reproducible bending behavior, etc., often completelymasked the effects caused by generated Coriolis forces, greatlydiminishing the practical use of a mass flow meter.

A mechanical structure and measurement technique which, among otheradvantages: (a) avoided the need to measure or control the magnitude ofthe angular velocity of a Coriolis mass flow rate instrument'soscillating flow conduit; (b) concurrently provided requisitesensitivity and accuracy for the measurement of effects caused byCoriolis forces; and (c) minimized susceptibility to many of the errorsexperienced in earlier experimental mass flow meters, is taught in U.S.Pat. Nos. Re 31,450, entitled "Method and Structure for FlowMeasurement" and issued Nov. 29, 1983; 4,422,338 entitled "Method andApparatus for Mass Flow Measurement" and issued Dec. 27, 1983; and4,491,025 entitled "Parallel Path Coriolis Mass Flow Rate Meter" andissued Jan. 1, 1985. The mechanical arrangements disclosed in thesepatents incorporate curved continuous flow conduits that are free ofpressure sensitive joints or sections, such as bellows, rubberconnectors or other pressure deformable portions. These flow conduitsare solidly mounted at their inlet and outlet ends, with their curvedportions cantilevered from the support. For example, in flow meters madeaccording-to any of the aforementioned patents, the flow conduits arewelded or brazed to the support, so that they are oscillated inspring-like fashion about axes which are located essentially contiguouswith the solid mounting points of the-flow conduits or, as disclosed inU.S. Pat. No. 4,491,025, essentially at the locations of solidlyattached brace bar devices designed to clamp two or more conduitsrigidly at points located forward of the mounting points.

By so fashioning the flow conduits, a mechanical situation ariseswhereby, under flow conditions, the forces opposing generated Coriolisforces in the oscillating flow conduits are essentially linear springforces. The Coriolis forces, opposed by essentially linear springforces, deflect or twist the oscillating flow conduits containingflowing fluid about axes located between and essentially equidistantfrom the portions of those flow conduits in which the Coriolis forcesmanifest themselves. T-he magnitude of the deflections is a function ofthe magnitude of the generated Coriolis forces and the linear springforces opposing the generated Coriolis forces. Additionally thesesolidly mounted, continuous flow conduits are designed so that they haveresonant frequencies about the oscillation axes (located essentially atthe locations of the mountings or brace bars) that are different from,and preferably lower than, the resonant frequencies about the axesrelative to which Coriolis forces act.

Various specific shapes of solidly mounted curved flow conduits aredisclosed in the prior art. Included among these are generally U-shapedconduits "which have legs which converge, diverge or are skewedsubstantially" (Re 31,450, col. 5, lines 10-11). Also disclosed in theart are straight, solidly mounted flow conduits which work on the samegeneral principles as the curved conduits.

As stated above, the Coriolis forces are generated when fluid is flowedthrough the flow conduits while they are driven to oscillate.Accordingly, under flow conditions, one portion of each flow conduit onwhich the Coriolis forces act will be deflected (i.e. will twist) so asto move ahead, in the direction in which the flow conduit is moving, ofthe other portion of the flow conduit on which Coriolis forces areacting. The time or phase relationship between when the first portion ofthe oscillating flow conduit deflected by Coriolis forces has passed apreselected point in the oscillation pathway of the flow conduit to theinstant when the second portion of that conduit passes a correspondingpreselected point in that pathway is a function of the mass flow rate ofthe fluid passing through the flow conduit. This time differencemeasurement may be made by various kinds of sensors, including opticalsensors as specifically exemplified in U.S. Pat. No. Re 31,450,electromagnetic velocity sensors as specifically exemplified in U.S.Pat. Nos. 4,422,338 and 4,491,025, or position or acceleration sensorsas also disclosed in U.S. Pat. No. 4,422,338. A parallel path doubleflow conduit embodiment with sensors for making the preferred timedifference measurements is described in U.S. Pat. No. 4,491,025. Thisembodiment provides a Coriolis mass flow rate meter structure which isoperated in the tuning fork-like manner earlier described in U.S. Pat.No. Re 31,450. Detailed discussion of methods and means for combiningmotion sensor signals to determine mass flow rate appears in U.S. Pat.Nos. Re 31, 450 and 4,422,338 and in application PCT/US88/02360,published as W089/00679.

In the aforementioned meter designs, the sensors are-typically placed atsymmetrically located positions along the inlet and outlet portions ofthe flow conduit which provide acceptable sensitivity to enable theselected sensors to make measurements yielding a mass flow rate that isaccurate within +/- 0.2 percent.

On the order of about 100,000 Coriolis mass flow meters have been builtusing the inventions of one or more of U.S. Pat. Nos. Re 31,450,4,422,338 and 4,491,025 and these meters have had extensive commercialuse. More than ten years' experience in the commercial application ofthese meters to mass flow rate measurement with a variety of diversefluid products has shown that in general, the end users are satisfiedwith the sensitivity and accuracy of their performance but desire thatthe meters be improved in overall stability, including zero stability,thus reducing plant maintenance related to these meters, including meterrecalibration. Meter instability, in general, results fromsusceptibility of the meters to the unwanted transfer of mechanicalenergy from sources external to such meters. Such forces can also affectthe zero (i.e., measured value at no flow) stability of the flow meters.

While commercial experience as described above has shown essentially noproblem in practical use with fatigue failure of the flow conduits, itis recognized that potential improvements in conduit life span byreducing possible sources of fatigue failure represent a forward step.Similarly, providing a sealed pressure-tight case increases thesuitability of the meters for hazardous materials applications atsignificant pressures which may range up to 1,000 psi and even higher.Even when achievable pressure rating is balanced against costconsiderations involved in fabricating the case, the use of a case asherein described affords a pressure rating for the meter at least ashigh as 300 psi for flow tube outside diameter sizes up to about 21/2inches and as high as 150 psi for larger sized flow tubes.

SUMMARY OF THE INVENTION

The present invention provides an improved mass flow meter withconsiderably increased overall stability, including reducedsusceptibility to external forces and increased zero stability, reducedpressure drop characteristics and better resistance to fluid pressures.A number of design changes to the Coriolis mass flow meters manufacturedin accordance with one or more of the previously cited patents haveresulted in optimizing their already successful features and operatingcharacteristics.

The present invention relates to Coriolis mass flow rate meters thatinclude one or more flow conduits which are driven to oscillate at theresonant frequency of the flow conduit containing fluid flowingtherethrough. The drive frequency is maintained at this resonance by afeedback system, heretofore described, which detects a change in theresonant behavior of the fluid-filled conduit as a result of the fluidmass change due to changes in fluid density. The flow conduits of theseCoriolis mass flow rate meters are mounted to oscillate about anoscillation axis located substantially at the mounting points or at thelocation of the brace bars. The resonant frequency of oscillation isthat associated with the oscillation axis. The flow conduit also deforms(twists) about a second axis which is that axis about which the flowconduit deflects or twists in response to Coriolis forces generated as aresult of the flow of fluid through the oscillating flow conduit. Thislatter axis associated with Coriolis-caused deflections is substantiallytransverse to the oscillation axis. The present invention provides animproved flow meter with enhanced stability having reducedsusceptibility to the influence of outside forces, primarily because ofoptimized sensor placement as explained more fully hereinafter. Otherimprovements which contribute to overall stability of the improved meterinclude reducing by at least fourfold the mass of the sensors anddriver.

In a preferred embodiment, a modified U-shaped flow conduit design isprovided, having two essentially straight inlet and outlet legs whichconverge towards each other at the process line manifold, and bends, attwo symmetrical locations along the length of the conduit, separated byan essentially straight middle portion. It is also contemplated thatsome modified U-shape flow conduits will have convergent inlet andoutlet legs which are separated by a continuously curved middle portion,rather than a straight middle portion and that others will havesubstantially parallel inlet and outlet legs in accordance with currentcommercial embodiments. Attached to each flow conduit at symmetricallocations are two motion sensors, so located that the susceptibility toexternal forces of the signals which they detect and transmit to themeter electronics is dramatically reduced over that of previously knowncommercial mass flow meters. This is accomplished in one preferredembodiment by locating the motion sensors between but as close aspossible to the nodes on each side of the conduit of the second out ofphase twist mode and the third out of phase bending mode of the flowtube and placing the driver equidistant between these sensors. Themasses-of the motion sensors plus their mountings and of the driver plusits mounting are substantially reduced in relation to the correspondingparts of the mass flow meters heretofore in commercial use. Thesusceptibility of the flow conduit to fatigue failure may optionally bereduced by providing novel brace bars having a novel nipple shapedsleeve, which serve to define the axis about which each flow conduitoscillates, but conventional brace bars may alternatively be used and insome embodiments, brace bars are omitted. In one embodiment, advantagemay be taken of the convergent U-shape to provide a wafer configurationmanifold structure, without flanges, for connecting to the process lineto be monitored. A special sealed pressure tight case is provided whichencloses the flow conduit, motion sensors, driver and associatedelectrical connectors. Several embodiments of such a case are disclosedherein, among which the embodiment of FIGS. 8 and 9 is preferred.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an optimized Coriolis mass flow meter of thisinvention partially within a case

FIG. 1A illustrates the location of the motion sensors as a result ofmodal analysis for the FIG. 1 embodiment.

FIGS. 2A and 2B illustrates an option novel brace bar configuration.

FIG. 3 illustrates an optimized Coriolis mass flow meter of thisinvention with a wafer manifold structure partially within a case asshown by FIG. 4;

FIG. 4 illustrates an optional high pressure case design; and

FIGS. 5A-7I illustrate shaker table stability test results.

FIG. 8 illustrates another optional high pressure case design which ispreferred based on cost and ease of fabrication.

FIG. 9 gives further detail regarding the FIG. 8 case design.

FIGS. 10-10F and 11A-11L illustrate further test results as hereinafterdescribed.

DETAILED DESCRIPTION OF THE INVENTION INCLUDING THE DRAWINGS

The major feature of the present invention the minimization of theinfluence of external forces upon meter stability--is achieved throughoptimal placement of sensors and, to a limited extent, of brace bars. Ithas been found that there are essentially six modes of vibration, withinthe frequency range of 0 to 2000 Hz, excitation of which is likely toresult in loss of meter stability. They are identified as (1) the firstin phase bending mode (of lower frequency than the drive frequency), (2)the first out of phase bending mode, which corresponds to thefundamental drive frequency, except that the drive frequency is thenatural frequency of the fluid--filled tube (whereas modal analysis isconducted on the empty tube), (3) the first out of phase twist (alsocalled torsion or deflection) mode, (4) the second out of phase twistmode, (5) the second out of phase bending mode and (6) the third out ofphase bending mode. Optimal placement of sensors is achieved byconducting a modal analysis of the flow tube to locate the two nodes foreach of the six modes on that tube and to determine, based upon tubegeometry, size and material, those node points to which the sensorsshould be placed most closely proximate. For a flow tube of thegeometric configuration shown in FIG. 1, for example, modal analysis hasshown the sensors should optimally be placed intermediate the second outof phase twist node and the third out of phase bending node on eitherside of the flow tube, as close to each of these nodes as possible.Those skilled in the art will appreciate that, depending upon thegeometry and other characteristics of the flow tube, node points for thesix enumerated modes may be located differently in relation to oneanother. In some flow tube shapes, two or more node points of differentmodes may actually coincide, making it possible to locate sensors at thelocation of coincidence and thereby enhancing flow tube sensitivity. Thepresent invention embraces the discovery, as a rule of thumb, that meterstability is enhanced by locating the sensors as close as possible oneach side of the tube to at least two node points, each of which is anode point for a different one of the modes above, and especially ofthose designated (3) and (6) above. The invention further embraces thediscovery that the influence of mode 1, the first in phase bending mode,may be minimized or eliminated by a placement of the brace bars whichseparates harmonics of mode 1 from those of mode 2.

FIG. 1 illustrates a preferred embodiment of a Coriolis mass flow meterof optimized modified U-shape and motion sensor positioning andmounting. As in the current commercial meters, the flow conduits 112 aresolidly mounted to the manifold 130 at points 131. Brace bars 122, aresolidly mounted to the flow conduits 112, thereby defining oscillationaxes B' when the flow conduits 112 are driven in tuning fork fashion bydriver 114. When flowable material flows through conduits 112, theCoriolis forces cause the conduits to deflect about deflection axes A'.Electrical connectors 125 from the driver, 126 from motion sensors 118,and 127 from motion sensors 116 may be connected and supported in stablestress minimizing fashion to bracket 128 as shown, or alternatively thebracket may be dispensed with as discussed hereinafter, in favor ofprinted circuit boards mounted to the case. The connectors shown in FIG.1 are individual wires or ribbon-shaped flexible connectors withembedded wires, which are mounted in a stable, stress minimizinghalf-loop shape. It is contemplated that flexible connectors, asdescribed in U.S. patent application Ser. No. 865,715, filed May 22,1986, now abandoned; its continuation U.S. patent application Ser. No.272,209, filed Nov. 17, 1988, now abandoned, and its continuation U.S.patent application Ser. No. 337,324, filed Jul. 10, 1989, may be used.Such flexible connectors also provide a stable, stress minimizinghalf-loop shape. In FIG. 1, experimental motion sensors 116 are locatedat the ends of the inlet or outlet leg 117 just before the bend. Motionsensors 118 are located at a position determined by modal analysisaccording to this invention, which effectively minimizes the influenceof external forces. In a commercial meter embodiment, only motionsensors 118 would be present and motion sensors 116, used experimentallyfor comparison purposes, would be eliminated. The meter of FIG. 1includes case 140 which encloses the flow conduit and associatedattachments and is fixed to the manifold 130, but it is contemplatedthat a meter case as shown in FIG. 4 or FIG. 8 and described below mightpreferably be used.

Another feature of the flow meter design for the embodiment of FIG. 1which minimizes the effects of external forces involves balancing of theflow conduits and their attachments and employing reduced mass sensorand driver components.

In Coriolis mass flow meters, the flow conduits serve as springs, withthe spring forces acting predominantly on the inlet and outlet legs. Theflow conduits of the FIG. 1 embodiment are of modified U-shape having nopermanent deformation from bending in the inlet and outlet legs. Nobending during the fabrication process results in the absence ofpermanent deformation in the four regions in which spring forces act inthe double conduit meters. As a result, all four regions displayessentially the same response to spring forces if similar materials ofessentially the same dimensions are used. This improves the ability ofthe flow meter manufacturer to balance the flow conduits. Balance of theflow conduits is further enhanced by decreasing the masses of the motionsensors and driver by using lighter mass magnets and coils and reducingthe size of their mountings.

The motion sensors and drivers are comprised, as in current commercialmeters, of a magnet and a coil. The sensors are of the type disclosed inU.S. Pat. No. 4,422,338 which linearly track the entire movement of theconduit throughout its oscillation pathway. In the FIG. 1 embodiment andin other embodiments of this invention, the total mass of these sensorsand of the driver are reduced over their total mass in currentcommercial meter embodiments by a factor of at least about 4 andpreferably by a factor of 5 to 6 or more. This reduction in mass isaccomplished by use of a lightweight bobbin having molded pinconnections and by winding the coil with 50 gauge wire while continuingto use the same mass magnets. The lightweight sensors and driver aremounted directly on the flow conduits, thus eliminating mountingbrackets. The lightweight coil used, e.g., in a meter embodiment of thesize and shape of that in FIG. 1 with a flow tube of approximately 0.25inch outside diameter, has a mass of approximately 300 milligrams. Priorcoils used with comparable sized mass flow meters made pursuant to U.S.Pat. Nos. Re. 31,450, 4,422,338 and 4,491,025 and having approximatelythe same flow tube outside diameter size had a mass of approximately 963milligrams. In the same sized meter embodiment according to FIG. 1, thenew assemblies add a total of approximately 3.9 grams to the mass flowmeter (1 driver coil and 2 sensors coils at 300 grams each, and 3magnets at 1 gram each). By contrast, in comparable earlier commercialembodiments, the corresponding assemblies added 22.2 grams (1 drivercoil, 2 sensor coils, 1 coil bracket, 1 magnet bracket and 3 magnets) tothe mass flow meter.

For the FIG. 1 embodiment, a representative modal analysis wasperformed. As one result thereof, the second out of phase twist modenode and the third out of phase bending mode node were located on a flowconduit having the dimensions and properties shown in Table 1 below andon FIG. 1A:

                  TABLE 1                                                         ______________________________________                                        Conduit material:    316L   stainless                                                                     steel                                             Conduit length:      16     inches                                            Conduit outer diameter:                                                                            .25    inch                                              Conduit wall thickness:                                                                            .010   inch                                              Inlet leg:           3      inches                                            Outlet leg:          3      inches                                            Middle Section:      5      inches                                            Bend radius:         1.25   inches                                            ______________________________________                                         The resulting sensor location which is midway between the aforesaid mode      nodes, was placed at 22.5° measured from the horizontal axis           extending from the bend radius centerpoint.                              

This resulting sensor location is not only between, but in the closestpossible proximity to each of the two node points, on each side of theconduit. As those skilled in the art will readily appreciate, byperforming modal analyses on flow conduits of other precise shapes,dimensions and materials, each of the node points for all of the modesenumerated above can be located and resulting sensor locations canreadily be optimized.

In some embodiments of the improved meters of this invention, thefundamental driving frequency (the first out of phase bending mode) isincreased relative to current commercially available flow meters made byapplicants' assignee, thereby increasing the values of its harmonics.This results in better separation of the individual harmonics for thedrive mode from that of other modes. In the FIG. 1 embodiment of thesize stated, for example, the harmonics of the other five modes ofinterest are each separated from harmonics of the driving frequency byat least 20 Hz, for all frequencies below 2000 Hz.

In the FIG. 1 embodiment, the placement of the brace bars has the effectof separating the first in phase bending frequency from the fundamentaldriving frequency and thereby eliminating possible effects of excitationof the first in phase bending frequency. The effects of external forcesoperating at frequencies corresponding to the remaining four modes ofinterest are in part minimized by the balanced flow conduit design. Inaddition, the effects of the second out of phase twist mode and thethird out of phase bending mode are also minimized in this embodiment bylocating the motion sensors between, but in close proximity to the nodesof both these two modes, which nodes happen to be located closetogether. It is contemplated that other location selections can be madeto minimize the effects of those modes that most affect stability of anyparticular conduit, taking into account through modal analysis its size,shape and material.

Testing of the FIG. 1 embodiment of the current commercial Model Dmeters manufactured by applicants' assignee and of current commercialCoriolis mass flow meters manufactured by others at varying fluidpressures ranging from less than 10 psi up to about 1000 psi establishedthat at fluid pressures approaching 1000 psi, variations in drivefrequency and twist frequency are induced which adversely affect theaccuracy of mass flow measurements. To date, it has been determined thatthese effects of high fluid pressure are minimized by increasing theflow tube wall thickness by approximately 20% and by enclosing the flowtube assembly in a specially designed fluid-pressure-insensitive case,as discussed below.

Applying the wall thickness increase to the meter embodiment of FIG. 1,for example, for a tube of outside diameter 0.230 inches, the wallthickness is increased from about 0.010 inches to about 0.012 inches inorder to minimize instabilities caused by high fluid pressure.

FIG. 2 shows an optional brace bar design according to this invention.Each brace bar 122 is formed, as by punching a piece of metal (e.g.,316L or 304L stainless steel) or other suitable material, to provide twosleeves with nippled transitions 121 from holes having the outerdiameter of flow conduit (hole 124), to larger holes 120. These bracebars are contemplated to be brazed or welded to the flow conduits inorder to reduce stress concentrations at the point of attachment 123,the primary locus about which the conduit is oscillated. It is withinthe scope of the present invention, however, to utilize conventionalbrace bars as earlier disclosed in the art.

FIG. 3 shows an optimized Coriolis meter as in FIG. 1, with an explodedview of the process line attachment. Instead of the typical prior artflanged manifold, a novel wafer flangeless structure 230 is provided forwhich the ends 232 can be bolted between the existing flanges in amanufacturing or other commercial process line, by means of threadedconnectors 234 passing through flange holes 238 and held in place bynuts 235.

FIG. 4 illustrates one form of case which minimizes pressure effects.This form can be used to enclose the entire flow conduit and sensorattachment assembly. It comprises a pipe 350 of sufficient diameter toenclose the flow conduits 312, driver, motion sensors and associatedwire attachments (not shown). The pipe is bent in the shape of the flowconduit. It is then cut longitudinally into two essentially equalhalves. The flow conduits 312 are fitted into it along with theassociated driver, motion sensors and wiring. The other half is fittedover this combined assembly and welded along the two longitudinal seamsand at the connections to the manifold. Thus, a pressure tight case isprovided which is suitable for applications involving hazardous fluidcontainment and able to withstand significant pressures on the order ofat least 300 psi and up to 500 pounds per square inch or more. For someembodiments, a printed circuit board may be attached to the inside ofthe case, with flexible connections running from the driver and motionsensors to the circuit board. A junction box may then be attached to thecase and connected to the circuit board by wires which can be runthrough pressure tight fittings at the top of the case. The junction boxis in turn connected to means for processing electronically the signalsfrom the sensors to give mass flow readout values and, optionally fluiddensity readout values.

An alternative case, preferred for ease of fabrication, is shown in FIG.8 and a section thereof is shown in FIG. 9. This form of case is madefrom stamped steel pieces of half-circular cross section as shown inFIG. 9, (which depicts a piece 2 or 4 from FIG. 8) welded together toform the case. As specifically applied to the embodiment of FIG. 1, thiscase is formed of ten pieces labelled 1-10 on FIG. 8 which are assembledin the following manner:

Five pieces (1, 2, 3, 4 and 5 as labelled on FIG. 8) comprising one halfof the case--i.e., when assembled covering one half the outercircumference of the flow tube--are welded to the support comprising theinlet-outlet manifold of the flow tube. Printed circuit boards, notshown in any of the figures, are affixed to the case at locations asnear as possible to the placement of the pick-off coil portions of thesensors on the flow tube and the pick-off coil terminals are connectedto these printed circuit boards by flexures containing wires of the typereferred to hereinabove or by individual half-loop shape wires. Wiresare then run along the case to the center straight section of the case(i.e. section 3 which encloses the straight flow conduit section 112 ofFIG. 1) where the wiring feed-through to the meter electronics islocated. This feed-through, which is not shown in FIGS. 8 and 9, maycomprise posts to which the wires are directly connected or may comprisea third printed circuit board to which the wires are connected and whichis, in turn, connected to feed-through posts and then to a junction box,not shown, positioned on section 3 of the case at its midsection. Afterthe wiring is completed, the remaining five pieces (not shown in FIG. 8,which is a plan view of the case) are welded in place to one another, tothe support and to the previously assembled and welded portion,preferably by means of automated welding. These latter five piecescomprise one half of the case. The welds between pieces are as shown bythe lines on FIG. 8. In addition, welds are made along the inner andouter periphery of the case at seam lines which are not shown, but whichconnect the top and bottom halves of the case both inside the enclosureformed by the meter tube and support and outside that enclosure.

The case embodiments of FIGS. 4, and 8 are illustrative only. Thoseskilled in the art will readily recognize that similar cases can readilybe fashioned to any size and shape of curved or straight tube Coriolismass flow meter and that, depending upon the precise shape involved, theembodiment of FIGS. 8 and 9 may advantageously be made with othernumbers of stamped steel half-circumferential pieces. As is also readilyapparent, other wiring arrangements may be readily devised by thoseskilled in the art without departing from the essential principles ofthis invention.

Shaker table tests were performed to test the influence of externalvibration forces and process line noise in exciting the flow conduitwith its associated attachments. Such external forces are frequentlypresent during plant operations. FIGS. 5A through 5F show experimentalshaker table test results for a current commercial Micro Motion, Inc.Model D25 Coriolis mass flow meter. FIGS. 6A through 6F show results forsimilar tests for a current commercial Micro Motion, Inc. Model D40meter. The Model D25 has a 0.172 inch inner diameter flow conduit; theD40 has a 0.230 inch inner diameter. FIGS. 7A through 7I showexperimental test results for similar tests for a Coriolis mass flowmeter similar to that shown in FIG. 1.

In each of FIGS. 5A through 7I, the x-axis is the axis through the meterflanges (i.e., parallel to the oscillation axis B'--B'), the y-axis isparallel to the plane of the flow conduits (i.e., parallel to thedeformation axis A'--A'). The z-axis is perpendicular to the plane ofthe flow conduits. The parameters of interest are summarized in Table 2:

                  TABLE 2                                                         ______________________________________                                                       Vert.             Vert.                                             Full Scale                                                                              Scale Freq.                                                                             Electronics                                                                           Scale % of                                        Flow Rate Sweep     output  Full Scale                                                                            Motion                               FIG. (lbm/min) (Hz)      (mA)    Range   Axis                                 ______________________________________                                        5A   1.04                4.20     10     z                                    5B   10.4                4.20    100     z                                    5C   --        15-2000   --      --      z                                    5D   1.04                4.20     10     x                                    5E   10.4                4.20    100     x                                    5F   --        15-2000   --      --      x                                    6A   1.04                4.20     10     z                                    6B   10.4                4.20    100     z                                    6C   --        15-2000   --      --      z                                    6D   1.04                4.20     10     x                                    6E   10.4                4.20    100     x                                    6F   --        15-2000   --      --      x                                    7A   1.04                4.20     10     x                                    7B   10.4                4.20    100     x                                    7C   --        15-2000   --      --      x                                    7D   1.04                4.20     10     z                                    7E   10.4                4.20    100     z                                    7F   --        15-2000   --      --      z                                    7G   1.04                4.20     10     y                                    7H   10.4                4.20    100     y                                    7I   --        15- 2000  --      --      y                                    ______________________________________                                    

These shaker table experiments were performed on complete mass flowmeter assemblies without cases. The output indicated on the strip chartrecordings of FIGS. 5A through 7I are of motion sensor readings inresponse to the corresponding external vibration. The sequence shown ineach series of charts is the meter's response to a linear frequency rampranging from 15 Hz to 2 KHz and then vibration inputs at randomfrequencies (FIGS. 5C, 5F, 6C, 7C, 7F, 7I). The frequency ramp occursover a ten minute period and random vibrations occur over anapproximately five minute period. FIGS. 5A, 5B, 5D, 5E, 6A and 6B eachindicate the influence of external vibrations of various frequencies inexciting harmonics of the six modes of motion of the D25 and D40 metersthat are discussed above.

FIGS. 7A through 7F show susceptibility to excitation due to externalvibrations of a meter of this invention of the FIG. 1 embodiment aboutthe x and z axes (the same axes as in FIGS. 5A through 5F) and are tothe same respective scale. FIGS. 7G through 7I are taken about they-axis. (The random vibrations were conducted first in FIGS. 7D-7F). Itis noted that the optimized meter shows dramatically reduced influenceof external vibrations in exciting harmonics of the six modes of motion.Thus, the optimized design is shown effectively to isolate the metersfrom effects of external forces.

In addition, tests were performed to test the influence of externalvibrations on zero stability. Such tests provided results for thestability of the time difference (Δt) measurement at no flow, theso-called jitter test. A frequency counter was used to directly measurethe pulse width of an up/down counter prior to any averaging orfiltering of the electronics. The test was performed on a shaker tableusing random frequency input over a range of accelerations in the x, y,and z directions. The results showed that, as the accelerations wereincreased, the influence of external vibrations resulted in pulse widthdivergence of one or more multiples of the average value from theaverage value for both the D25 and D40 meters. Such divergence, for eachaxis, is markedly reduced for the optimized meter. Thus, as in the caseof the vibration tests, the jitter tests showed that the optimized meterdesign effectively isolates the meters from the effects of externalforces.

FIGS. 10A-10G inclusive are plots of further data obtained with a flowmeter embodiment constructed as in FIG. 1, having conventional bracebars and a 20% thicker flow tube than comparably sized currentcommercial meters, as herein disclosed, with sensors placed inaccordance with the teachings of this invention between, but as near aspossible to the node points of the modes labelled as 4 and 5 hereinabove. As tested, the flow tube of this flow meter embodiment was halfcovered (i.e., one half of the circumference of the pipe) by a case ofthe type shown in FIGS. 8 and 9, and a junction box (not shown in thedrawings) was appended to the outside of the case where the wires feedthrough the case. The junction box was conventionally connected toanother box (called the "remote flow transmitter" or "RFT") containingthe meter electronics and having readout panels for mass flow rate anddensity values, from which data was collected for FIGS. 10A-10Dinclusive. The inner diameter of the flow tube wall on this meterembodiment was approximately 0.206 inches.

FIGS. 10A and 10B each represent calibration plots of accuracy versusflow rate using water at mass flow rates from 0 to 45 pounds per minute.FIG. 10A differs from FIG. 10B in that FIG. 10A represents a "22 point"calibration curve with the first measured points taken at mass flowrates of about 3 to 4 pounds per minute. FIG. 10B covers a "45 point"calibration curve in which more data points, especially for mass flowrates below 5 pounds per minute, (commencing at about 0.5 pound perminute) were collected.

FIG. 10B also shows fluid line pressure drop data as measured for massflow rates from 0 to about 45 pounds per minute. FIGS. 10A and B combineto show that the meter embodiment of this invention performs well withinthe published accuracy values of ±0.2% which characterize the currentcommercial meters of applicants' assignee, Micro Motion, Inc. FIG. 10Balso illustrates the very acceptable fluid line pressure dropperformance of this meter embodiment.

FIGS. 10C and D are, respectively, plots of measured mass flow rate anddensity analog drift values against fluid pressure of water at valuesfrom 0 to approximately 2000 psi. In each instance, a comparison appearson the plot of average historical standard deviation measurements forcommercial mass flow meters of the D-series sold by Micro Motion, Inc.In FIG. 10C, flow rate analog drift and flow rate standard deviationdata points are shown in units of seconds. In FIG. 10D, density analogdrift and density standard deviation are shown in units of grams percubic centimeter. In both cases, the data show the meter built inaccordance with this invention to perform well within the measuredstandard deviation data.

FIGS. 10E, F and G are plots of shaker table test data obtainedsimilarly to the data depicted in FIGS. 5A to 7I, but presented as plotsof shaker table frequency (in Hertz) against analog output (i.e. massflow rate) disturbance in seconds, whereas FIGS. 5A to 7I arereproductions of strip charts plotting shaker table frequency in Hertzagainst motion sensor readings per se. In addition, the data in FIGS.10E, F and G were collected on the same meter assembly with half caseattachment as that to which FIGS. 10A-D inclusive apply. For comparisonpurposes, similar plots for two different D25 flow conduit units, eachwithout case attachment, are presented in FIGS. 11A-11L inclusive. Ineach instance, the x, y and z - axes are as defined above, the shakertable vertical scale frequency sweep is from 15 to 2000 Hertz, theremote frequency transmitter from which analog output data were obtainedhad a span of 5 grams per second and a calibration factor of 1. Otherparameters of interest are summarized in Table 3:

                  TABLE 3                                                         ______________________________________                                              Sweep of the                                                                  Vibration  Motion                                                       FIG.  Table      Axis     Unit                                                ______________________________________                                        10E   log        x        Embodiment of this invention                        10F   "          y        Embodiment of this invention                        10G   "          z        Embodiment of this invention                        11A   linear     x        Model D25 Unit 1                                    11B   log        x        Model D25 Unit 1                                    11C   linear     y        Model D25 Unit 1                                    11D   log        y        Model D25 Unit 1                                    11E   linear     z        Model D25 Unit 1                                    11F   log        z        Model D25 Unit 1                                    11G   linear     x        Moded D25 Unit 2                                    11H   log        x        Moded D25 Unit 2                                    11I   linear     y        Moded D25 Unit 2                                    11J   log        y        Moded D25 Unit 2                                    11K   linear     y        Moded D25 Unit 2                                    11L   log        y        Moded D25 Unit 2                                    ______________________________________                                    

A linear sweep of the vibration table expends the same amount of time inmoving through each 100 Hertz vibration interval so that, e.g. a sweepof 15 to 115 Hertz occurs in the same time interval as e.g. 1000 to 1100Hertz. In log sweep, an amplified time interval is consumed at lowfrequencies, e.g., from 15 to 400 Hertz and a shortened (or speeded up)time interval is consumed at the higher frequency end. In bothinstances, the total sweep time is the same. As can be seen, log sweepclearly points out the frequencies at which external excitations havegiven rise to harmonic disturbances in current commercial Model Dmeters. FIGS. 10E, F and G show the meters of this invention to bemarkedly less susceptible to such influences than the D25 flow conduits.

Although the preferred embodiment is illustrated for a dual flow conduitmass flow meter, it is contemplated that the invention described hereincan be embodied in a Coriolis mass flow meter having only one flowconduit, either in conjunction with a member such as leaf spring, or adummy conduit, that forms a tuning fork with the flow conduit or undercircumstances where the single flow conduit is of very small mass and ismounted to a base of relatively very large mass.

While the foregoing detailed discussion focuses, for exemplary purposes,upon one size and shape of flow tube, numerous changes and modificationsin the actual implementation of the invention described herein will bereadily apparent to those of ordinary skill in the art, and it iscontemplated that such changes and modifications may be made withoutdeparting from the scope of the invention as defined by the followingclaims.

We claim:
 1. A mass flow meter for flowable materials wherein mass flowrates for flowable materials are determined based on at least onemeasured effect of Coriolis forces, said flow meter comprising: asupport means; at least one continuous flow conduit which is free ofpressure sensitive joints or sections, each of said conduits beingsolidly mounted to said support means at inlet and outlet ends for saidconduits; driver means for oscillating each of said conduits aboutbending axes adjacent each of said solid mountings; a pair of sensormeans mounted on each of said conduits for monitoring motion of saidconduits while flowable materials are flowing therethrough and saidconduits being oscillated by said driver means about said bending axes,monitored motion including motion caused by Coriolis forces about twistaxes for each of said conduits, said sensor means generating signalsrelated to all motions of said conduits; and signal processing means todetect and convert said signals to mass flow rate values; in which theimprovement comprises:fixed mounting of each of said pair of sensormeans on each of said conduits to monitor motions of said conduitsincluding motions about said twist axes, where each sensor means ismounted between nodes of a pair of vibration modes for said conduit,said pair of vibration modes being selected from a pairing of the firstin phase bending mode, first out of phase bending mode, first out ofphase twist mode, second out of phase twist mode, second out of phasebending mode, or third out of phase bending mode.
 2. A mass flow meteraccording to claim 1 in which said continuous flow conduit has anessentially straight inlet leg and an essentially straight outlet legwhich converge toward one another at said support and are interconnectedopposite said support by the remainder of said continuous conduit.
 3. Amass flow meter according to claim 2 in which said inlet and outlet legsare interconnected opposite said support by an essentially straightportion of said conduit which curves at either end to meet each of theessentially straight leg portions.
 4. A mass flow meter according toeither of claim 2 or claim 3 in which members of said sensor pairs areplaced between nodes of the second out of phase twist mode and thesecond out of phase bending mode on the respective inlet and outletsides of each flow conduit.
 5. A flow meter according to claim 1 havingat least two flow conduits clamped together by brace bars at pointsalong the inlet and outlet legs which are spaced from the support, saidpoints having been determined by modal analysis to be those points whichprovide optimum separation between the frequencies of the first in phasebending mode and the first out of phase bending mode so as to minimizeeffects of the first in phase bending mode on meter sensitivity.
 6. Aflow meter according to claim 5 in which said continuous flow conduithas an essentially straight inlet leg and an essentially straight outletleg which converge toward one another at said support and areinterconnected opposite said support by the remainder of said continuousconduit.
 7. A flow meter according to claim 5 in which the brace barsinclude nipple shaped mounting sleeve means.
 8. A flow meter accordingto either of claim 2 or claim 3 having at least two flow conduits,wherein the support comprises a flangeless inlet and outlet plenum whichfurther comprises two separated flow chambers, one for flow separationon the inlet side and one for flow recombination on the outlet side. 9.A flow meter according to claim 1 further comprising a pressure tightcase of essentially the same geometric configuration as said flowconduit which encases all of said conduit, said sensor means and saiddriver, and is welded to said support.
 10. A flow meter according toeither of claim 2 or claim 3 further comprising a pressure tight case ofessentially the same geometric configuration as said flow conduit whichencases all of said conduit, said sensor means and said driver, and iswelded to said support.